Uniqueness and Sharp Estimates on Solutions to Hyperbolic Systems with Dissipative Source
Global weak solutions of a strictly hyperbolic system
of balance laws in one-space dimension were constructed
(cf. Christoforou [C])
via the vanishing viscosity method
under the assumption that the source term g is dissipative.
In this article, we establish sharp estimates
on the uniformly Lipschitz semigroup P
generated by the vanishing viscosity limit
in the general case which includes also non-conservative systems.
Furthermore, we prove uniqueness of solutions
by means of local integral estimates
and show that every viscosity solution can be
constructed as a limit of vanishing viscosity approximations.